I present a new interpretation of Wittgenstein's later philosophy of logic and mathematics. This interpretation, like others, emphasizes Wittgenstein's attempt to reconcile platonistic and constructivistic approaches. But, unlike other interpretations, mine explains that attempt in terms of Wittgenstein's position about the relations between our concepts of necessity and provability. If what I say here is correct, then we can rescue Wittgenstein from the charge of naive relativism. For his relativism extends only to provability, and not to necessity.

This collection provides a complete version of Shelley's masterpiece Frankenstein as well as her short fiction and letters.

Shelley Weinberg argues that the idea of consciousness as a form of non-evaluative self-awareness helps solve some of the thorniest issues in Locke's philosophy: in his philosophical psychology, and his theories of knowledge, personal identity, and moral agency. The model of consciousness set forth here binds these key issues with a common thread.

Witty, sexy and radiantly beautiful, the Shelley translationof Plato's great Dialogue on Love is by far the best in theEnglish language. It has been described as conveying "much of the vivid life, the grace of movement, and the luminous beauty of Plato" -- "the poetry of a philosopher rendered by the prose of a poet." Although a masterpiece in its own right, the Shelley translation was suppressed and then bowdlerized for well over a century. In 19th century Britain, (...) male love -- at the heart of the dialogue -- was unmentionable. The Banquet and Shelley's accompanying essay, "A Discourse on the Manners of the Antient Greeks," were not published in their entirety until 1931, and then in an edition of 100 copies intended "for private circulation only." The Pagan Press edition is complete, authentic and readable. For the first time this work has received the editing and typography it deserves. (shrink)

Cecilea discusses with Shelley Tremain her experience as a first-generation U.S. citizen and first-generation university graduate; why she was motivated to study philosophy and become a professional philosopher; the launching of the new, open access, online journal, the Journal of Philosophy of Emotions (JPE); the “mismatch” between what she seemed like “on paper” and what she is is capable of; how societal, institutional, professional, and philosophical practices and policies must be adjusted to enable others like her to flourish as (...) professional philosophers; and any resources—such as articles, books, and videos—that she would like to recommend on the topics and issues that she has addressed in this interview. (shrink)

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse (...) Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. (shrink)

This paper explores different interpretations of the word ‘deep’ as it is used by mathematicians, with a large number of examples illustrating various criteria for depth. Most of the examples are theorems with ‘historical depth’, in the sense that many generations of mathematicians contributed to their proof. Some also have ‘foundational depth’, in the sense that they support large mathematical theories. Finally, concepts from mathematical logic suggest that it may be possible to order certain theorems or problems according to ‘logical (...) depth’. (shrink)

This article is a feminist intervention into the ways that disability is researched and represented in philosophy at present. Nevertheless, some of the claims that I make over the course of the article are also pertinent to the marginalization in philosophy of other areas of inquiry, including philosophy of race, feminist philosophy more broadly, indigenous philosophies, and LGBTQI philosophy. Although the discipline of philosophy largely continues to operate under the guise of neutrality, rationality, and objectivity, the institutionalized structure of the (...) discipline implicitly and explicitly promotes certain ontologies, epistemologies, and methodologies as bona fide philosophy, while casting the ontologies, epistemologies, and methodologies of marginalized philosophies as mere simulacra of allegedly fundamental ways of knowing and doing philosophy and thus rendering these marginalized philosophies more or less expendable. This article is designed to show that legitimized philosophical discourses are vital mechanisms in the problematization of disability. (shrink)

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a (...) large extent, the story of philosophy of mathematics. (shrink)

In two studies, we used the Ethics Position Questionnaire (EPQ) to investigate the relationship between individual differences in moral philosophy, involvement in the animal rights movement, and attitudes toward the treatment of animals. In the first, 600 animal rights activists attending a national demonstration and 266 nonactivist college students were given the EPQ. Analysis of the returns from 157 activists and 198 students indicated that the activists were more likely than the students to hold an "absolutist" moral orientation (high idealism, (...) low relativism). In the second study, 169 students were given the EPQ with a scale designed to measure attitudes toward the treatment of animals. Multiple regression showed that gender and the EPQ dimension of idealism were related to attitudes toward animal use. (shrink)

The following three related contributions jointly serve to lift up elements of the thought of the anthropolo­gist Gregory Bateson that can be fruitfully compared with elements of Michael Polanyi’s thought. In a brief introduction, William Stillwell reviews Bateson’s life and developing interests. Stillwell also provides, in a creative dialog form akin to Bateson’s own dialogs, a short review article on Noel Charlton’s Understanding Gregory Bateson: Mind, Beauty and the Sacred Earth. The third piece is Jere Moorman’s short 1991 (...) essay (now out of print) discussing Polanyi’s ideas about tacit knowing and their connection with Bateson’s ideas about the double bind. (shrink)

According to the perspective developed in this article, widely shared, hegemonic cultural beliefs about gender and their impact in what the authors call “social relational” contexts are among the core components that maintain and change the gender system. When gender is salient in these ubiquitous contexts, cultural beliefs about gender function as part of the rules of the game, biasing the behaviors, performances, and evaluations of otherwise similar men and women in systematic ways that the authors specify. While the biasing (...) impact of gender beliefs may be small in any one instance, the consequences cumulate over individuals’ lives and result in substantially different outcomes for men and women. After describing this perspective, the authors show how it sheds newlight on some defining features of the gender system and illustrate its implications for research into specific questions about gender inequality. (shrink)

Serena Olsaretti brings together new essays by leading moral and political philosophers on the nature of desert and justice, their relations with each other and with other values.

Locke’s account of personal identity has been highly influential because of its emphasis on a psychological criterion. The same consciousness is required for being the same person. It is not so clear, however, exactly what Locke meant by ‘consciousness’ or by ‘having the same consciousness’. Interpretations vary: consciousness is seen as identical to memory, as identical to a first personal appropriation of mental states, and as identical to a first personal distinctive experience of the qualitative features of one’s own thinking. (...) There is wide agreement, however, that Locke’s theory of personal identity is meant to complement his moral and theological commitments to a system of divine punishment and reward in an afterlife. But these commitments seem to require also a metaphysical criterion, and Locke is insistent that it cannot be substance. The difficulty reconciling the psychological and metaphysical requirements of the theory has led, at worst, to charges of incoherence and, at best, to a slew of interpretations, none of which is widely accepted. (shrink)

How the concept of proof has enabled the creation of mathematical knowledge. The Story of Proof investigates the evolution of the concept of proof--one of the most significant and defining features of mathematical thought--through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence (...) on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as "infinitesimal algebra," and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field's power and progress. (shrink)

The default theory of aesthetic value combines hedonism about aesthetic value with strict perceptual formalism about aesthetic value, holding the aesthetic value of an object to be the value it has in virtue of the pleasure it gives strictly in virtue of its perceptual properties. A standard theory of aesthetic value is any theory of aesthetic value that takes the default theory as its theoretical point of departure. This paper argues that standard theories fail because they theorize from the default (...) theory. (shrink)

Wellman argues that legitimate states have a presumptive right to close their borders, excluding all prospective immigrants. He maintains that this right is not outweighed by egalitarian considerations because societies can fulfill their duties to outsiders by transferring aid instead of opening borders. I argue that societies cannot discharge their egalitarian duties by providing aid in at least two cases: when opening borders is the only way to fulfill these duties, and when transferring aid is inconsistent with egalitarian commitments. I (...) also consider additional, non-egalitarian moral considerations that may justify a duty to maintain open borders. I conclude that Wellman fails to prove that states have an actual, all things considered right to close their borders. (shrink)

This is the first of the four essays in Part II of the book on liberalism and traditionalist education; all four are by authors who would like to find ways for the liberal state to honour the self-definitions of traditional cultures and to find ways of avoiding a confrontation with differences. For example, Shelley Burtt argues that the liberal state has good reason to be far more accommodating of traditional groups than liberals commonly recognize. She contends that liberal autonomy, (...) properly understood, is not threatened in any special way by traditional religious or cultural groups, and that traditional cultures are as capable of fostering autonomy as their more cosmopolitan counterparts. Most strikingly, she maintains that it is a good thing, from the perspective of liberal autonomy, to be encumbered by unchosen attachments and loyalties such as those that we might expect to be most fully developed within religious communities. The essay is in two main parts: Part One takes up the challenge of the notion that liberal theorists have missed the chance to describe in detail the possibilities for autonomous thought from within a comprehensive education to a particular way of life or understanding of the good, offering several reasons why the central demand of autonomy – to think and know for oneself – is well within the reach of individuals who receive this sort of ‘grounded’ education; Part Two looks more closely at liberal theories of autonomy, particularly aspects of those accounts that encourage the idea that comprehensive educations are at odds with the development of autonomy, arguing that such characterizations overstate the difficulties that exist, and concluding by reaffirming the possibility of combining an education for autonomy with education toward a comprehensive vision of the good life. (shrink)

Locke’s theory of personal identity was philosophically groundbreaking for its attempt to establish a non-substantial identity condition. Locke states, “For the same consciousness being preserv’d, whether in the same or different Substances, the personal Identity is preserv’d” (II.xxvii.13). Many have interpreted Locke to think that consciousness identifies a self both synchronically and diachronically by attributing thoughts and actions to a self. Thus, many have attributed to Locke either a memory theory or an appropriation theory of personal identity. But the former (...) stumble on circularity and the latter is insufficient for Locke’s moral theory insofar as he is committed to a theory of divine rectification. The common problem is that Locke’s theory seems to demand an objective, or metaphysical, fact of a continuing consciousness that does not appeal to a traditional notion of substance for the continuity. I’m suggesting something new. In II.xxvii of the Essay, we see an ambiguity in Locke’s use of the term ‘consciousness’. Locke seems to see consciousness as both a mental state by means of which we are aware of ourselves as perceiving and as the ongoing self we are aware of in these conscious states. First, I make the textual argument why we should read Locke as having a conception of a metaphysical fact of a continuing consciousness that does not appeal to thinking or bodily substance to establish its continuity. I then argue that the metaphysical fact of an enduring consciousness is revealed to us as a phenomenological fact of experience. Due to the nature of certain kinds of perceptual situations we have an experience of ourselves as temporally extended. Although the text bears out that Locke seemed to think there is a fact of an ongoing consciousness, I argue that it is consistent with his reluctance elsewhere that he makes no further epistemological or ontological claims about it. Finally, I provide an account of Locke’s understanding of memory and its relation to consciousness that supports the claim that consciousness is something ontologically distinct from either thinking or bodily substance. (shrink)

One hundred sixty subjects acted as members of a hypothetical Institutional Animal Care and Use Committee and evaluated five proposals in which animals were to be used for research or educational purposes. They were asked to approve or reject the proposals and to indicate what factors were important in reaching their ethical decisions. Gender and differences in personal moral philosophy were related to approval decisions. The reasons given for the decisions fell into three main categories: metacognitive statements, factors related to (...) the animal, and factors related to the design of the experiment. (shrink)

Critical diversity studies (CDS) can be found within “traditional,” or “established,” university disciplines, such as philosophy, as well as in relatively newer departments of the university, such as African studies departments, women’s and gender studies departments, and disability studies departments. In this article, therefore, I explain why philosophy of disability, an emerging subfield in the discipline of philosophy, should be recognized as an emerging area of CDS also. My discussion in the article situates philosophy of disability in CDS by both (...) distinguishing this new subfield’s claims about disability from the arguments about disability that mainstream philosophers make and identifying the assumptions about social construction and antiessentialism that philosophy of disability shares with other areas of CDS. The discussion is designed to show that a (feminist) philosophy of disability that draws upon the work of Michel Foucault will transform how philosophers understand the situation of disabled people. By drawing upon Foucault, that is, I offer philosophers of disability and other practitioners of CDS a new understanding of disability as an apparatus of power relations. -/- . (shrink)

Given his representationalism how can Locke claim we have sensitive knowledge of the external world? We can see the skeptic as asking two different questions: how we can know the existence of external things, or more specifically how we can know inferentially of the existence of external things. Locke's account of sensitive knowledge, a form of non-inferential knowledge, answers the first question. All we can achieve by inference is highly probable judgment. Because Locke's theory of knowledge includes both first order (...) psychological and second order normative conditions, sensitive knowledge can be non-inferential and less certain than intuitive and demonstrative knowledge. (shrink)

Hilbert took to using ideal elements in the 1890's, in both algebraic number theory and geometry. His Zahlbericht of 1897 popularized the concept of the ideal introduced by Dedekind in 1871 (which in turn formalized the concept of "ideal number" introduced by Kummer in the 1840's). His geometric work likewise followed a long history of ideal elements, some that originated in geometry and others that originated elsewhere and were applied to geometry. Important examples were:Piero della Francesca's Ideal City.Points at infinity (...) in projective geometry, originating in the 1430s from the "vanishing points" in perspective drawing.Imaginary points in algebraic geometry, originating from the imaginary numbers used by .. (shrink)

In “Why Should Liberals Care about Equality?,” Ronald Dworkin distinguishes between two forms of liberalism, one form based on neutrality, and the other one based on equality. As Dworkin explains it, proponents of both forms argue against legal incursion into private morality, and argue in favour of increased sexual, political, racial, and economic equality; however, they disagree about which of these traditionally liberal values is the fundamental one, and which is its derivative. Liberalism based on neutrality takes as its fundamental (...) value that one which holds that government must remain neutral with respect to moral issues, and it supports egalitarian measures only insofar as they can be shown to derive from that constitutive principle. For liberalism based on equality, the fundamental value is that one which holds that government must treat each of its citizens as an equal; egalitarian liberalism insists upon moral neutrality only to the extent that equality requires it. (shrink)

A multiple analogy is a structured comparison in which several sources are likened to a target. In "Multiple analogies in science and philosophy," Shelley provides a thorough account of the cognitive representations and processes that participate in multiple analogy formation. Through analysis of real examples taken from the fields of evolutionary biology, archaeology, and Plato's "Republic," Shelley argues that multiple analogies are not simply concatenated single analogies but are instead the general form of analogical inference, of which single (...) analogies are a special case. The result is a truly general cognitive model of analogical inference.Shelley also shows how a cognitive account of multiple analogies addresses important philosophical issues such as the confidence that one may have in an analogical explanation, and the role of analogy in science and philosophy.This book lucidly demonstrates that important questions regarding analogical inference cannot be answered adequately by consideration of single analogies alone. (shrink)

Locke has been accused of failing to have a coherent understanding of consciousness, since it can be identical neither to reflection nor to ordinary perception without contradicting other important commitments. I argue that the account of consciousness is coherent once we see that, for Locke, perceptions of ideas are complex mental acts and that consciousness can be seen as a special kind of self-referential mental state internal to any perception of an idea.

In response to the concern that ethnically diverse immigrants are not being sufficiently integrated into receiving liberal democratic societies, liberal nationalists have offered two specific naturalization policy proposals. The first would require naturalizing immigrants to assimilate the national culture of the receiving society; the second would encourage newcomers to adopt the prevailing civic national identity. This paper rejects these proposals. In contrast to liberal nationalists, I deny that good citizenship presupposes a common culture or civic national identity and I develop (...) a non-nationalist naturalization model that would encourage immigrants to become integrated into liberal democratic societies by participating in their major socio-economic and political institutions and practices. (shrink)

If, as Richard Wollheim says, the Acquaintance Principle is ‘a well-entrenched principle in aesthetics,’ it would be surprising if there were not something true at which those who have asserted it have been aiming. I argue that the Acquaintance Principle cannot be true on any traditional epistemic interpretation, nor on any usability interpretation of the sort Robert Hopkins has recently suggested. I then argue for an interpretation of the principle that treats acquaintance as the end to which judgments of aesthetic (...) value are the means as opposed to the other way around. (shrink)

Ikujiro Nonaka, whose formative experience is Japanese, is an established scholar who has written about large business organizations. He sees knowledge at the heart of the organization and its products and aims to develop Michael Polanyi’s conception of tacit knowledge in a practical direction to enhance organizational “knowledge creation.” For Nonaka, what matters is the practice, the doing, the embodiment of knowledge. An organization can amplify and crystallize individuals’ tacit knowledge in a process that allows them to experience deeper understanding. (...) Nonaka holds that it is iimportant to explore the potential that knowledge holds. His spiral process describes disciplined practices that make tacit knowledge independent and available to restructure the organizational knowledge context. (shrink)

Introduced into the philosophical lexicon during the Eighteenth Century, the term ‘aesthetic’ has come to be used to designate, among other things, a kind of object, a kind of judgment, a kind of attitude, a kind of experience, and a kind of value. For the most part, aesthetic theories have divided over questions particular to one or another of these designations: whether artworks are necessarily aesthetic objects; how to square the allegedly perceptual basis of aesthetic judgments with the fact that (...) we give reasons in support of them; how best to capture the elusive contrast between an aesthetic attitude and a practical one; whether to define aesthetic experience according to its phenomenological or representational content; how best to understand the relation between aesthetic value and aesthetic experience. But questions of more general nature have lately arisen, and these have tended to have a skeptical cast: whether any use of ‘aesthetic’ may be explicated without appeal to some other; whether agreement respecting any use is sufficient to ground meaningful theoretical agreement or disagreement; whether the term ultimately answers to any legitimate philosophical purpose that justifies its inclusion in the lexicon. The skepticism expressed by such general questions did not begin to take hold until the later part of the 20th century, and this fact prompts the question whether (a) the concept of the aesthetic is inherently problematic and it is only recently that we have managed to see that it is, or (b) the concept is fine and it is only recently that we have become muddled enough to imagine otherwise. Adjudicating between these possibilities requires a vantage from which to take in both early and late theorizing on aesthetic matters. (shrink)

Global migration raises important ethical issues. One of the most significant is the question of whether liberal democratic societies have strong moral obligations to admit immigrants. Historically, most philosophers have argued that liberal states are morally free to restrict immigration at their discretion, with few exceptions. Recently, however, liberal egalitarians have begun to challenge this conventional view in two lines of argument. The first contends that immigration restrictions are inconsistent with basic liberal egalitarian values, including freedom and moral equality. The (...) second maintains that affluent, liberal democratic societies are morally obligated to admit immigrants as a partial response to global injustices, such as poverty and human rights violations. This article surveys the main philosophical arguments for these positions on immigration and discusses the critical responses to these arguments. (shrink)